If A is an acute angle and cot A + cosec A = 3, then the value of cos A is equal to:
1. 4/5
2. 3/5
3. 1/5
4. 2/5
1. 4/5
2. 3/5
3. 1/5
4. 2/5
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Correct Answer – Option 1 : 4/5
Given:
cot A + cosec A = 3
Formula used :
cosec2 A – cot2 A = 1
cosec A – cot A = 1/ ( cosec A + cot A)
cot A + cosec A = 3 ……(eq1)
cosec A – cot A =1/3 …….(eq2)
By solving eq 1 and eq 2 By elimination
2 cosec A = 3 + 1/3
cosec A = 5/3 = H / P
\({H^2} = {P^2} + {B^2}\)
\({5^2} = {3^2} + {B^2}\)
B2 = 25 – 9
B2 = 16
base = 4
cosA = 4/5